Debt is too a burden on our children (unless you believe in Ricardian Equivalence)

So, I was out there shovelling snow, thinking about writing a post on the burden of the debt on future generations. And about how macroeconomists' beliefs on this question had silently shifted about 30 years ago, and about how we as a profession have engaged in a sort of "memory falsification" (like Timur Kuran's concept of "preference falsification"), because we didn't want to admit that we now believe something we used to believe only unsophisticated economically illiterate rubes believed.

And I then I thought "Nah, what's the point of rehashing old ground?. Nobody nowadays believes that old "we owe it to ourselves" stuff that we used to believe."

And then I came inside and read Paul Krugman's blog post. Now I absolutely have to write the post I had decided not to write.

"That’s not to say that high debt can’t cause problems — it certainly can. But these are problems of distribution and incentives, not the burden of debt as is commonly understood. And as Dean says, talking about leaving a burden to our children is especially nonsensical; what we are leaving behind is promises that some of our children will pay money to other children, which is a very different kettle of fish."

Sorry, but that's just plain wrong. The economically illiterate rube who thinks that the national debt is a burden on our children or grandchildren is basically right. It's the exact opposite of "especially nonsensical". Unless you believe in Ricardian Equivalence.

"And you don’t have to be a right-winger to acknowledge that yes, very high marginal tax rates act as a disincentive to productive activity. So real GDP may well fall significantly.

This is what I mean when I say that the burden of debt is about incentives, not about having to deliver resources to other people.

......

The general point is that the analogy with a family that owes too much is all wrong. Unfortunately, this dumb analogy dominates our national discourse."

And I'm saying that it's not (just) about incentives, and it is about having to deliver resources to other people, and that the analogy with the family is not dumb and not all wrong (even though, like all analogies, it doesn't work perfectly).]

In the olden days we all used to believe NB. At least, all educated sophisticated people believed NB. Only uneducated unsophisticated people believed B. But we all smugly knew that "the man in the street" was wrong. In fact, a quick test for whether someone was educated and sophisticated was whether he believed B or NB. Maybe a few of us educated sophisticated people might have believed B, or didn't really understand why NB was so obviously correct, but we kept our beliefs secret, because we didn't want other people to think we were uneducated or unsophisticated rubes.

I can still remember an economics seminar at Carleton, sometime in the 1980's. The visiting speaker was an older guy, an old-school Keynesian from one of the top US universities (I have forgotten his name). Halfway through the seminar, he said "I assume that the audience here is economically literate, and that nobody here believes B?" He paused and glared around the room. The blood went to my face (a grad student told me afterwards my face was red). I raised by hand, and said that I believed B.

James Buchanan was not a sophisticated macroeconomic theorist. He didn't do macro. He did political economy/public choice. He had zero authority in macro theory. James Buchanan argued for B. But he was just a farmboy, like me. (Yes, I do have a slight chip on my shoulder; why do you ask?)

Then, all of a sudden, it seemed like all the educated sophisticated people switched to believing B. It was a very quiet revolution. There were no visible signs of argument at all. One day we all (I mean all we educated sophisticated people) believed NB; and the next day we all believed B. And we all stopped our smug condescension about the poor ignorant "person on the street" who believed B. In fact, we never mentioned the fact that we all used to believe NB. We wiped our old beliefs from our memories, like Soviet photographs. It was just too embarrassing to talk about.

There's a danger to this sort of memory wiping, and silent shifts in belief. Some people never got the memo, and still believe the old NB like we all (all educated sophisticated people) did once. Plus, it says something about our beliefs in general if we all just believe what it is fashionable to believe. (And we do, very often, which is why many of our beliefs, especially educated sophisticated beliefs, really suck).

Paul Krugman is a much better economist than me. But he never got this memo. It's time to re-open this old box of suppressed memories.

Let me make some simplifying assumptions so we can get to the heart of the distinction between B and NB. (Yes of course these assumptions are false and unrealistic, but by excluding areas where we agree we can focus on the area where we disagree.)

Suppose the government makes a transfer of 100 apples to the current cohort, financed by borrowing. Does that create a burden on future generations? Yes or no? B or NB?

I say Yes. I say B. It does create a burden on future generations. The only case where it does not create a burden on future generations is where Ricardian Equivalence holds. According to Ricardian Equivalence, the person in the street realises it will create a burden on future generations, and so saves the whole of the transfer payment, including interest, passes it on as a bequest to his children, who pass it on to their children, precisely because he wants to offset that burden on future generations.

The person on the street, in his unsophisticated uneducated ignorance, is basically right. The debt is a burden on his kids, or grandkids. Only if he anticipates that burden, and decides to offset it by increasing his bequests, a la Barro-Ricardo, does he eliminate that burden

No. My argument does not involve time travel. It doesn't require we can take apples grown 100 years from now, put them in a time-machine, send them back in time, and eat them today. But it is as if we could.

My argument is obvious. At least, it's obvious to anyone who has thought about overlapping generations models. And it's equally obvious to the unsophisticated uneducated rube who has never thought about overlapping generations models.

The government borrows 100 apples from each of cohort A, then gives each person in cohort A a transfer payment of 100 apples. It is exactly as if the government had simply given each person in cohort A an IOU for 100 apples. That IOU is a bond.

So far there is no change in cohort A's consumption of apples.

Cohort A then sells the bonds to the younger members of cohort B. So each person in cohort A gets an extra 110 apples (assume 10% interest per generation), which he eats. Cohort A then dies.

Cohort A is better off. Each member of cohort A eats an extra 110 apples. In present value terms, those extra 110 apples are worth 100 apples at the time the transfer payment is made.

Cohort B eats 110 fewer apples when young, but 121 extra apples when old, and they sell their bonds to cohort C. Although cohort B eats 11 more apples in their lifetimes, the present value of their total consumption of apples is the same. The rate of interest must be high enough to persuade them to eat fewer apples when young and more apples when old, otherwise they wouldn't have bought the bonds from cohort A. So cohort B is not worse off.

But (given my assumption) the debt is rising faster than GDP. The government knows this is unsustainable. It cannot rollover the debt forever, because eventually the next cohort will be unable to buy the bonds from the older cohort. So the government decides to pay off the debt by imposing a tax of 121 apples on each young person in cohort C, which it uses to buy back the bonds from cohort C.

Each member of cohort C eats 121 fewer apples.

Cohort A eats more apples, and cohort C eats fewer apples. It is exactly as if apples travelled back in time, out of the mouths of cohort C into the mouths of cohort A. (With interest subtracted as they travel back in time through the time machine.)

Yes, the national debt is a burden on future generations.

Can that burden on future generations be offset in some cases? Yes.

Ricardian Equivalence means that inviduals decide to offset the burden by each cohort giving rather than selling their bonds to their kids in the next cohort. So if you believe in Ricardian equivalence, you can consistently argue that the national debt is not a burden. But it's only not a burden because individuals see it is a burden and take offsetting action. That ignorant uneducated person in the street is still right.

And if the debt is used to finance investment in the kids' education then the burden is offset.

And if the interest rate is permanently less than the growth rate then the "No Ponzi" condition does not hold, and the debt can be rolled over with interest forever without taxing future generations, so cohort A eats more apples and no subsequent cohort eats fewer apples (there is never a cohort like cohort C, they are all like B).

I can relax all the other simplifying assumptions, and show that the basic message is still roughly the same. But not today.

Comments

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Good post. I'd add that distortionary taxes are a huge issue, which Krugman just sweeps under the rug with an aside about "incentives." He knows his readers won't understand this, and hence assume he means the debt actually is not a burden in the real world, not just that it's not a burden in an imaginary world free of distorting taxes.

I suppose Krugman might believe in Ricardian equivilence for debt, but certainly not money.

Scott: thanks. What's your memory on this? Do you remember the silent shift in beliefs on this?

I can distinctly remember believing NB as an undergrad, then reading Barro and Buchanan in the late 1970's and early 1980's, spending ages getting my head around it, and then switching to believing B. And noticing most other macroeconomists believing B too. But it was almost never discussed.

1) Why do you assume that the debt grows more quickly, on a persistent basis, than GDP?

2) Why do you assume that the gov't will levy taxes to pay off the debt? Isn't that the key assumption that makes the debt a burden?

By assumption (I suppose) the debt is owed to some citizens (in the long run foreign exchange flexibility keeps debt owed to foreigners at low levels, right?). So the gov't decides to tax the populace as a whole to pay those creditors. How come? Because they own everybody else (in effect)? Isn't it really a distributional question?

Isn't the assumption that the gov't will pay off the debt at odds with history? Andrew Jackson did it in the U. S. in 1835 and drained a lot of Spanish dollars out of the economy by not accepting bank notes toward the end. How well did that work out? In retrospect, was that not a major factor in the depression of 1837 - 1843?

Your story is a perfect description of a Pay As You Go pension scheme. The first generation gets high consumption when young (don't have to pay premiums) and high consumption when old (get benefits). Subsequent generations get lower consumption when young (pay premiums), compensated for with higher consumption when old (get benefits).

The "B" scenario happens when, due to low population growth rates and low productivity growth rates, the PAYG pension scheme becomes unsustainable, so there's a generation that pays premiums into the plan, but doesn't collect the benefits they were promised, because when they're old there aren't enough younger workers to sustain the PAYG plan. (My guess: the B generation will be the people born right at the end of, or just after, the baby boom).

This is a different scenario, I think, from the one described by Krugman, "what we are leaving behind is promises that some of our children will pay money to other children, which is a very different kettle of fish."

From a political point of view, I can see why people might want to avoid talking about social security and Medicare entitlements. But, as they say, if something can't go on indefinitely, it won't.

The gov't "cannot rollover the debt forever, because eventually the next cohort will be unable to buy the bonds from the older cohort."

That's what I mean by saying that some people (the older cohort) "own" the rest (the younger cohort). If the younger cohort is too poor to buy the gov't bonds, it's because the older cohort has too much money, right? They have impoverished their own children.

Min: "P and NP" are sometimes used as shorthand for "some proposition P and its opposite Not P". I just switched to B from P, because B represents "Burden". But they were sort of meant to stand for any general belief, as well.

"1) Why do you assume that the debt grows more quickly, on a persistent basis, than GDP?

2) Why do you assume that the gov't will levy taxes to pay off the debt? Isn't that the key assumption that makes the debt a burden?"

If the government never needs to increase taxes to pay the debt, or interest on the debt, then there is no (simple) burden on future generations. And the government needs to increase taxes if and only if 1 is true. (Otherwise you can leave taxes the same, and the debt grows at rate r, but GDP grows at rate g, so the debt/GDP ratio still falls, so it's sustainable forever.

Normand: it doesn't really matter whether real interest rates are positive or negative. What matters is whether they are greater or less than the GDP growth rate. (If real interest rates are negative, it's more likely they will be below the growth rate.)

Frances: Yep. Debt-finance, relative to tax finance, is just like a PAYGO scheme. The only difference is that the interest rate on debt is market-determined, and the assets are marketable, so it's like being able to sell your future CPP benefits when you want to.

Burden:
1980 - CohortA borrows (consumes) from CohortB (forgoes consumption)
1990 - CohortB borrows (consumes) from CohortC (forgoes consumption)
2000 - CohortD not interested in lending; CohortC unable to borrow and enjoy the expected outcome of delayed gratification. (And CohortD would not be interested in lending if interest rates vs growth prospects aren't favourable.)
Underlying assumption, at some point there will be a generation that is required to pay for the consumption of the previous generation without any offsetting benefit.

Is that a correct interpretation of the problem? Does the point of debate hinge on the willingness of future generations to forgo current consumption in exchange for delayed but greater consumption?

Money isn't like apples. You can print more at any time (and now, without even needing paper) if the will is there. Money is trust and promises, not real resources like food or goods. To attempt to explain money with "stuff" is non-sensical to this layman. Its like trying to explain how a car works, except I will use a fish as a model.....

Can anyone here point to ANY case in the entire 2500 history of money in which one generation found itself impoverished by previous ones merely for accumulating money debt to themselves, as opposed to say taking actions that actually destroyed the means of production (through war or evnvironmental degredation) or because the debt was owed to a more powerful outside force? Cause I can't think of a single damned one, and if economics is supposed to be a social "science" capable of answering questions about the material world as it exists (as opposed to an imagined theoretical world no one inhabits) then maybe it should try to explain things that are actually possible.

Given how badly economics seems to have performed lately, maybe that moment when "everyone" began to "believe in B" again was a moment people lost sight of reality and decided to believe in stories again. How is that a good thing?

The critical assumption here is full employment. I don't think Krugman would deny that, if the current generation uses up resources that could otherwise be used for the benefit of future generations, then future generations will be worse off. (I usually think of the resources as potential capital investment diverted to consumption, but in your model it would be apples that keep getting consumed by the older generation during each period until the one after the government pays off its debt.) But Krugman is not talking about resources; he's talking about borrowing in the purely financial sense. As a practical matter, most of your assumptions are innocuous, but the full employment assumption is dramatically at variance with today's reality in a way that matters for Krguman's point. We can eat more apples. The apples, which didn't exist before the government borrowed, will appear through the magical process known as labor market clearing. This does not in any way reduce the number of apples available in the future.

In a sense you and Krugman (and Baker, from whom Krguman gets the argument) are both right. You're right because you've been explicit about your assumptions. He's right because his implicit assumption is more relevant to the issue at hand than is your explicit one. He should have put in a caveat, "This doesn't work if there's full employment."

Actually, you can make arguments that it doesn't work even without full employment, as long as the central bank's reaction function has certain characteristics. I've convinced myself that the reality is somewhere in-between. That is, some fraction of the debt is a burden on future generations, and that fraction depends on the central bank's reaction function, which I take to be such that the fraction is somewhere on the open interval between 0 and 1. Closer to zero I would guess, although if I were arguing with Noah Smith I would guess it's closer to one.

I might be misunderstanding your model. The crux seems to be that each generation has to be paid a little bit more in order to persuade them to voluntarily postpone their consumption, and that all these little-bit-mores will cumulatively provoke a collapse. Debt grows faster than GDP.

There would be obviously no problem if we dictated by fiat that each generation reduce their first-period apples by X (and buy X worth of bonds) and increase their second-period apples by X (and sell X worth of bonds). The contention is that each generation won't do that, because they have to be paid to alter their optimal time-preference? You had a ponzi negative-real-rate model a while ago where each generation sees it as an unambiguous improvement instead, so the real interest on the bonds can be zero. No collapse.

The lesson I'm seeing here is not "debt unambiguously imposes a burden"; it's "don't sell bonds that promise a higher nominal interest rate than the expected growth rate in nominal GDP". Promising a higher rate imposes a cumulative burden; forward-looking investors don't even buy the first issue. Promising an equal rate imposes no burden; this is the Krugman scenario, purely redistributive within each generation. Promising a lower rate (that sells nonetheless) is eating a free lunch. Would that be right?

Ricardian equivalence has to be irrelevant; if it held, why would investors buy the damn things to begin with? The last generation won't touch them, so neither will the second-last, third-last, etc.

Peter: In your first example, where the debt is rolled over forever, including interest, and future taxes are never raised, then cohort A is better off and no future cohort is worse off. But this is only possible if the rate of interest is permanently below the growth rate in the economy. Otherwise, then yes. Either the government has to increase taxes, or else there's a default on the debt, or else the debt cannot be sold, and some future generation regrets having bought the bonds, and there's a burden.

Gepap: You've been reading too much Graeber. If there's a default on the debt, or if it's depreciated by inflation, or if the government increases taxes just enough to pay the interest only, and rolls over the principle, there is a burden on future generations.

And money is not the same as debt (something Graeber doesn't understand). And people only buy paper debt, when they could spend the money on apples instead, because they think they can sell the debt later for more money with which they can buy more apples to eat. It's you and Graeber who are confused by thinking about paper IOUs.

Wouldn't the argument extend to all debt - government and private? I believe your reasoning suggests that any debt, to the extent that it constitutes inter-generational borrowing, will be a burden on future generations. So is there a burden imposed on future generations regardless of whether it is the government borrowing to build a bridge or a private firm borrowing to build a toll road? Is there something specific to government debt that makes it more intergenerational?

If the lenders (partly the next generation) are earning market interest rates, are they worse off due to this debt they have voluntarily financed? Wouldn't interest rates be endogenous to the level of debt? Is it the possibility of long-run default that voluntary lenders have not taken into consideration (as with the unsustainable compulsory PAYGO scheme) that makes this debt a 'burden'?

I am sorry for having so many questions - your post makes me feel more ignorant than the economically illiterate rubes.

(I would also note in passing that the NPG condition is -- as you acknowledge -- critical and is also contrary to historical experience, in that government bond yields have tended to be lower than growth rates. I don't think this is what Krugman had in mind, but it's worth some attention. In the end, given the combination of my central bank parameter between zero and one and the empirical failure of the NPG condition, I would say that, for practical purposes, debts incurred today by the US government are approximately zero burden on future generations. Throw in hysteresis and they probably are a net benefit.)

Now assume KC model with unemployment when cohort A are alive, and full-employment when cohort C are alive. Then cohort A gets 200 more apples, and cohort C gets 121 fewer apples.

david: it's the higher taxes on future generations that are the burden. If you can run a sustainable forever Ponzi scheme, then you don't need future tax increases and so there's no burden.

"Ricardian equivalence has to be irrelevant; if it held, why would investors buy the damn things to begin with? The last generation won't touch them, so neither will the second-last, third-last, etc."

No. You need to distinguish individual rationality from collective rationality. It is collectively rational for cohort C to refuse to buy the bonds from cohort B, and so on. But it is individually rational for them to buy the bonds (at the right interest rate).

Min: "Doesn't that violate your no real growth assumption? Where do the extra 10 apples come from without real growth?"

Assume each cohort produces 1,000 apples. Then you can keep the debt growing until it hits 1,000.

primed: "Wouldn't the argument extend to all debt - government and private?"

No. When I borrow, it's *my* name on the IOU. I have to tax myself to repay my debt. When the government borrows, the name on the IOU is left blank. It is only filled in when the government decodes to increase taxes. The people whose name gets filled in might not be born yet.

"If the lenders (partly the next generation) are earning market interest rates, are they worse off due to this debt they have voluntarily financed? Wouldn't interest rates be endogenous to the level of debt?"

Roughly speaking, cohort B is neither better off nor worse off. They might be slightly better or worse off due to the endogenous interest rate effect. (Can't quite get my head around which).

"Is it the possibility of long-run default that voluntary lenders have not taken into consideration (as with the unsustainable compulsory PAYGO scheme) that makes this debt a 'burden'?"

Either default or taxes to repay it, or pay interest, is what makes the debt a burden.

"I am sorry for having so many questions - your post makes me feel more ignorant than the economically illiterate rubes."

It took me many many hours 30 years ago trying to get my head straight on all this. And I still have to stop and think. And I may still get stuff wrong.

Andy: Yep. If PK wanted to argue that the NPC is not satisfied, then OK. There isn't a burden in that case because future taxes need never be raised. But that's not what his post says. He talks about some future children paying higher taxes to other future children.

And the condition for a sustainable forever Ponzi scheme is...? If you can keep rolling over the debt, then you don't need to ever need to raise more taxes. It would be sustainable forever. That's the point. As long as the nominal growth rate of contributions is at least the promised interest rate, it is sustainable forever, and if nominal output keeps increasing, then the share of state spending can remain constant and there is no burden.

If technology keeps marching on, then it is quite likely welfare-improving to move resource claims forward.

Adam P.: I think I've got it right. Cohort C pays 121 apples to cohort B to buy the bonds. Then it gets taxed 121 apples, and given 121 apples to buy back the bonds. So, on net, it eats 121 apples less than it produces.

Andy: Yep. If PK wanted to argue that the NPC is not satisfied, then OK. There isn't a burden in that case because future taxes need never be raised. But that's not what his post says. He talks about some future children paying higher taxes to other future children.

Ooooh, now I see. Yeah, that would be a problem. He doesn't say "taxes", though, he says "money" - possibly just debt-rollover? So you might be reading too much into it.

david: but he says "But these are problems of distribution and incentives,.." which has to mean the distributional and incentive effects of taxes. And he says "...what we are leaving behind is promises that some of our children will pay money to other children..." which also has to mean taxes. The government is promising on behalf of future children.

I'm still a little confused may be because I am thinking in purely real terms.

When the government decides to increase taxes to pay off the IOU, wouldn't that be a transfer between people essentially alive at the same time? (although some may be older and some may be younger depending on the age profile of tax payers versus bond-holders).

If the government decides to default on the IOU, wouldn't that also be an unforeseen redistribution between people essentially alive at the same time (although again, some may be older and some may be younger depending on the age profile of tax payers versus bond-holders) because those who were supposed to pay the extra taxes simply don't need to anymore.

Is it the unforeseen and involuntary nature of redistribution that will occur in a future period that makes the debt a burden for future generations?

I greatly appreciate the clarity you bring and I hope I can save some of those hours with your explanation.

"Gepap: You've been reading too much Graeber. If there's a default on the debt, or if it's depreciated by inflation, or if the government increases taxes just enough to pay the interest only, and rolls over the principle, there is a burden on future generations.

And money is not the same as debt (something Graeber doesn't understand). And people only buy paper debt, when they could spend the money on apples instead, because they think they can sell the debt later for more money with which they can buy more apples to eat. It's you and Graeber who are confused by thinking about paper IOUs."

Debt and money are instruments of trust - they have no instrinsic existance or value, never have and never will. A debt can disappear merely by people forgetting it was there, for example. This is fundamentally not true of an apple. If you forget you had an apple in your pocket it will eventually decay and ruin your pants, leaving some real trace of its existance. If you forgot you lent your budy five bucks two years ago and so did he, that debt just vanished, completely. How can one act as if something that is purely ideal (exist only as an idea, a concept) can be rationally compared to stuff? And money is at the end of the day no less ideal than debt.

It is true that people act based on their ideas, so people act as IF money and debt were real, but in the end, they still aren't. If a person believes themselves to be on fire they might roll around on the floor trying to put it out. There would be no distinguishing difference in the behavior of that person and one that is actually on fire. But if you, asd a neutral observer, had to try to intervene, it would be insane to think that hey, they both behave in the same manner, so I should treat the two situations equally. Just because people are nuts doesn't mean you should buy into their insanity.

I have only read interviews of Graeber, but he at least attempts to marshall empirical evidence in the form of historical documentation, which is a lot more in keeping with the spirit of science than not doing so. This is not meant to be a criticism of this blog in particular, but a general criticism of the profession of economics as currently performed.

Not really. In the United States the choice to purchase a chunk of the debt load is not wholly voluntary - they have this Social Security Trust Fund artifice to maintain the pretense of an individual moral right to payouts. The interest rate still floats, mostly; there would be much screaming if the SSTF was being raided to keep the state solvent. What you get is one politically-appointed institution that gets to decide who in each generation makes the payments and who gets the payouts in a (somewhat) net-progressive way, and thence one has distribution and incentive problems up the wazoo.

Moi: "Doesn't that violate your no real growth assumption? Where do the extra 10 apples come from without real growth?"
Nick Rowe: "Assume each cohort produces 1,000 apples. Then you can keep the debt growing until it hits 1,000."
OK. Generation 1 lends 100 apples worth of money to the gov't, and gets back 110 apples worth. So it eats 1010 apples, 10 more than it produced. Meanwhile, Generation 2 is on course to eat 990 apples. So it lends 100 apples worth of money to the gov't and gets back 110 apples worth back. So it eats 1000 apples, exactly as much as it produced. Ditto Generation 3, etc., in sustainable fashion.

There is some real transfer from Cohort C to Cohort B. So government debt initiated when Cohort A was calling the shots will lead to Cohort C consuming fewer apples (if they are the generation that pays off the debt)and Cohort B consuming more apples.

B & C are alive at the same time and there is intergenerational redistribution (to the extent that bond holders and tax payers are from different generations) at some point in the future because of the actions of a government run by Cohort A.

david: "When the government decides to increase taxes to pay off the IOU, wouldn't that be a transfer between people essentially alive at the same time?"

Suppose the government taxes cohort D, to buy back the bonds owned by cohort C. D eats 121 fewer apples. C gets repaid the apples it had lent to B. So D gets the burden of the debt. It's still the case that A gets to eat more apples, and whoever gets the taxes eats fewer apples. All intervening cohorts are (roughly, except for interest rate effects) neither richer nor poorer.

"If the government decides to default on the IOU, wouldn't that also be an unforeseen redistribution between people essentially alive at the same time (although again, some may be older and some may be younger depending on the age profile of tax payers versus bond-holders) because those who were supposed to pay the extra taxes simply don't need to anymore."

If the government defaults when cohort C owns the bonds, instead of taxing C to buy back the bonds, it makes no difference to C. C still eats 121 fewer apples than they produce.

Gepap: sure. Money and debt are social constructions. Like Tinkerbell the fairy, they only are real because we think they are real, and so act as if they are real. But the same is true of government and taxes too. Everything we call "the economy" is just fairies. And it's fairies, all the way down.

Which is a fun topic to explore, and one day I will. But not on this post. Government and taxes and bonds are all real, because we think we are real, and give our imaginary property rights in real apples to other people because the imaginary government which we think is real tells us we must do this. These words aren't real either. But we all think they are.

Min: "Meanwhile, Generation 2 is on course to eat 990 apples. So it lends 100 apples worth of money to the gov't and gets back 110 apples worth back. So it eats 1000 apples, exactly as much as it produced."

No. Remember the interest is added to the debt, because the government hasn't increased taxes yet.

Cohort B produces 1,000 apples, gives *110* apples to cohort A to buy the bonds, then gets paid *121* apples by cohort C when B gets old and sells the bonds. 100, 110, 121, etc., will eventually exceed 1,000.

primed: not quite. Assume each cohort lives 2 periods. So old A's and young B's overlap. Old B's and young C's overlap. Young B's transfer 110 apples to old A's. Young C's transfer 121 apples to old B's.

Nick could just as easily have said that cohort D refused to roll the debt and the government (perhaps incapable of raising taxes) defaults.

then it's clear how cohort C gets screwed. They paid 121 apples for debt that they thought would pay them 133 apples when old, instead they got nothing.

It raises the question of why C bought the debt but that could be explained by a shock, say a drought, that reduces apple production so that D won't or can't roll the debt.

This story is consistent with the 10% interest rate, it compensates for the probability of default, but also changes nature of the burden. Each cohort rolled the debt because the interest rate was high enough to make up for the possibility that they'd get nothing back. C gets nothing back but wasn't really screwed, they bought a risky asset at a fair price and lost.

Nonethless, Nick's point is valid. Since the interest rate is higher than the growth rate then default eventually happens or the government thinks ahead and raises the tax revenue to retire the debt and thus expropriates some random cohort.

Again, uncertainty about which cohort eventually loses can mean that with a high enough interest rate the debt trades today. We still know with certainty that some future cohort will lose.

I see you addressed the default interpretation above, I was typing my comment at the time.

I think you do need to treat carefully how it works that the debt trades at all. In perfect forsight for example nothing happens at all, cohort B refuses to roll the debt and you get immediate default, then no intergenrational transfer.

The government borrows 100 apples from cohort A, pays the apples back to A as a transfer and then defaults on the bonds. No transfer of any kind.

Understood - thank you. So the debt can be justified (using the welfare function of the burdened cohort) only if current government expenditure benefits the last cohort more than the burden itself (i.e., if somehow current government expenses helped to increase future apple production) or if there is no last cohort.

Also, if the real interest rate is less than the growth rate, there is no need for a last cohort.

"If cohort A eats more than it produces, then SOMEONE has to eventually eat less than they produce, because, in the long run, eaten has to equal produced, and the deficit is not allowed to proceed to infinity."

@Phil - no. Rowe's argument requires a cumulative explosion of the debt load relative to GDP. By itself, moving resources one generation forward is not problematic - you get something like Hilbert's Grand Hotel, in which all resources are consumed but new guests can always be found more resources. In the long run, apples eaten is apples produces is infinite.

Government debt is a burden to our children because the government is primarily a welfare program for the elderly (with an army on the side). It's not the debt that burdens our children, it's the transfers. If government spending were done on all cohorts equally, there would be no transfer effect.

Moi: "Meanwhile, Generation 2 is on course to eat 990 apples. So it lends 100 apples worth of money to the gov't and gets back 110 apples worth back. So it eats 1000 apples, exactly as much as it produced."

Nick Rowe: "No. Remember the interest is added to the debt, because the government hasn't increased taxes yet.

"Cohort B produces 1,000 apples, gives *110* apples to cohort A to buy the bonds, then gets paid *121* apples by cohort C when B gets old and sells the bonds. 100, 110, 121, etc., will eventually exceed 1,000."

You are conflating cohorts with the gov't, and money with apples. My impression is that you have posited an inflationary environment, but you don't say so. (That's why I was vague about the amount of money required to buy so many apples.)

When you lose me, Nick, it is usually at the starting gate. Your assumptions do not make sense to me. You have created a situation in which each succeeding generation consumes a greater portion of a fixed output. Of course that will self destruct. You talk as though Krugman is making unrealistic assumptions. Maybe so. But how realistic are your assumptions?

@David: Right. That's what my "deficit is not allowed to proceed to infinity" clause represents: the fact that you can't just keep cohort A's debt around forever, because at some point the load becomes too big to carry.

AdamP. If the government announces that future taxes will be levied as a proportionate tax on bonds, then the whole thing unravels backwards, as you say, and nobody will ever buy the bonds originally. But if the future taxes are lump sum taxes on individuals, regardless of whether that individuals holds bonds (i.e. you can't avoid taxes by not buying bonds) then it is individually rational to buy bonds (as long as the interest rate is above your rate of time preference).

It's hard to explain this in words, especially in a sort of representative agent model. (Sort of goes back to your old post about the representative agent vs the average agent.)

primed: Yep. That's it.

Phil: Yep, I think so. Except that under some conditions (interest rate less than growth rate) the debt and deficit can proceed to infinity.

Min: "When you lose me, Nick, it is usually at the starting gate. Your assumptions do not make sense to me. You have created a situation in which each succeeding generation consumes a greater portion of a fixed output. Of course that will self destruct."

But such things do in fact happen all the time!

As I said above, there can be substantial uncertainty about which cohort will lose and if the interest rate is high enough to compensate for a cohorts prior probabality that they'll lose then the bonds can trade for a lot of generations.

Seems to me that all we need is that the interest rate on the debt is higher than the growht rate.

Phil@4:43: no, david is right. The assumption that drives this is that the interest rate is higher than the growth rate. Otherwise you could keep the debt around forever, as a percentage of output it would be going to zero.

A gets more apples than it produces, every other cohort gets fewer apples when young and more apples when old in such quantities that they're happy with the trade.

Andy: "Do we lose any relevant generality by assuming a unit multiplier and zero interest rate?"

Basically no. It's a lot simpler with a 0% interest rate. It's just you lose the No Ponzi Condition, but if you just *assume* the debt must revert to zero, even with 0% interest, that's OK.

So, assume a simple Keynesian Cross model with a unit tax multiplier and 0% interest and unemployment in all periods. Cohort A gets to produce and consume 100 extra apples when it spends its transfer. Cohort C gets to consume and produce 100 fewer apples when it cuts consumption to pay for the higher taxes. (There might be Keynesian demand spillovers in both directions on cohort B, depending on the timing of A's and C's consumption changes).

Oh, I think we do lose generality. That is the problem. The multiplier effect is producing extra consumption on the part of the current generation. If it's just a matter of "cut taxes and consume the tax cut," then the bonds become a bequest instead of being sold to future cohorts, so cohort C ends up equally well off, using their bequest to pay off the taxes (unless you want to argue that cohort B will sell the bonds to cohort C after receiving them as a bequest). Do you really believe that the tax multiplier is much greater than 1?

Andy, you don't need a multiplier to get cohort A more consumption. They get it from B who willingly sacrifice it for the chance to get more consumption (transfered from C) when they are old. Cohort C makes the transfer so they can get one from D when they are old.

All cohorts after A simply make a trade of less when young for more when old at the 10% interest rate.

A wins because they didn't ever need to make such a transfer when they were young, yet they receive a transfer when old.

@AdamP: "the deficit is not allowed to proceed to infinity" is a more general case of "the interest rate is higher than the growth rate."

"The interest rate is higher than the growth rate" is sufficient but not necessary. "The deficit is not allowed to proceed to infinity" is both necessary and sufficient.

Instead of "the deficit is not allowed to proceed to infinity," substitute "compounding is not allowed to continue forever." Maybe that'll make it clearer?

For instance, suppose the interest rate is NOT higher than the growth rate. But God comes down and says, "all accounts must be settled by the year 2149." God's proclamation is sufficient to ensure that someone bears a burden, because it prevents compounding from continuing to infinity.

@Phil - still no. Say zero interest and zero growth. The state runs zero deficit, except in the first period, where is creates a debt load which it rolls over until 2149 for free. The deficit never proceeds to infinity.

Phil, you said ""If cohort A eats more than it produces, then SOMEONE has to eventually eat less than they produce..."

David pointed out, correctly, that if the real interest rate is lower than the growth rate then in fact A eats more than it produces and yet no other cohort ever has to consume less than its production.

"All accounts must be settled by this finite date" would do it, but it's not identical to requiring that the deficit cannot go to infinity.

Regardless it would be an assumption, not a consequence, i.e., you would still need to reverse it so:

"If cohort A eats more than it produces, and all accounts must be settled by 2149, then SOMEONE has to eventually eat less than they produce, because, in the long run, eaten has be at most produced, and amount produced is finite."

Doesn't Krugman's second post allude to a model where the No-Ponzi Condition is, indeed, not satisfied and the 500% debt load is rolled over forever at an interest rate equal to the growth in NGDP? And the losses are, indeed, the ensuing Harberger triangles?

@AdamP (and @Nick) But if the multiplier is 1, then we are producing exactly 100 more apples. The number of apples produced and consumed in the first period both rise by 100. And I'm assuming full employment in future periods, so there is no change in the number of apples produced in future periods. Summed over all N periods, there are 100 more apples. If cohort A is only consuming 100 more apples (i.e. the multiplier is 1), then adding up requires that all other cohorts combined must be consuming the same number of apples as before. The only question is whether there is a transfer from cohort B to cohort C (or to D, E, F, etc. if it takes longer to pay back the debt).

In the first period cohort A is young but the trade is a wash, they pay 100 apples to buy the bonds and then receive the 100 back from the government. No extra apples and no transfer.

In the second period A is old and B is young. The debt is rolled, B buys it for 110 apples which go to A. A consumes 110 apples that they otherwise would not have, B conumes 110 apples less than they would have. Why does B take the trade?

Because in the third period the debt rolls again, C buys it for 121 apples which go to B. B has accomplished a trade of 110 fewer apples when young for 121 more when old. That's a reasonable trade. C has done the first leg of a similar trade.

In no period has the number of apples produced changed, A's consumption in period two went up by 110 but that was matched by B consuming 110 less, aggregate consumption was unchanged.

david: well, PK is talking about the disincentive effects of increased future taxes, so he cannot be assuming the debt plus interest is rolled over forever.

Andy: I think that's right. I lose it a little on who exactly gets to eat the extra apples. But if the tax multiplier is 1 in the original period, and 0 (because of full employment) when taxes are raised, then there must be extra apples, as you say.

If you assume NPG (or equivalently full repayment), then it doesn't make much sense to assume unemployment in all future periods. Would you run a primary surplus just to pay back the debt if we were still below full employment? (Of course I mean full employment in Keynesian Cross sense. For practical purposes, if you're out of a liquidity trap, that counts as full employment, because the central bank will offset the effects of fiscal policy.)

Nick, no. Consider the case where the government never raises taxes. D refuses to roll the debt and the government defaults on C.

There's never any extra apples, C (while young) paid 121 apples to B. C then gets nothing from D, so in that period C (now old) and D both just consume what they produce. C lost because they gave 121 apples to B and then the next period got nothing from D, but in no period did production of apples need to increase (provided it was always greater than 121).

david: well, PK is talking about the disincentive effects of increased future taxes, so he cannot be assuming the debt plus interest is rolled over forever.

No, no. The debt plus interest is rolled over forever. The model in the second post doesn't even have any increased current real consumption, it's literally the pure debt-as-private-assets-creation scenario that the MMT people obsess about. The future tax revenue is found by taxing bondholder income - the state is writing each individual an IOU and then taxing it back. The disincentive effect is the practical absence of lump-sum taxes, e.g., the state is giving you $100 and then taxing you a % of your wage to make back $100, so there is an increase in the marginal rate.

Distinguish between intergenerational transfers and intragenerational redistribution for the moment.

Moi: "When you lose me, Nick, it is usually at the starting gate. Your assumptions do not make sense to me. You have created a situation in which each succeeding generation consumes a greater portion of a fixed output. Of course that will self destruct."

@AdamP 5:15/5:20, @David 5:14: I mean the deficit is not allowed to go to infinity TIME, not that it's not allowed to go to infinity apples or dollars. As long as, at some point, all accounts have to be settled, someone has to produce more than they consume.

I should have phrased it better. What I mean is, the only way for this to work is if the debt can be passed on forever. If forever can't happen, then someone has a burden.

Phil: "What I mean is, the only way for this to work is if the debt can be passed on forever. If forever can't happen, then someone has a burden."

A couple of years ago I chanced across an account of a pension (I am not sure of the correct term) granted by one of the French kings in perpetuity to a nobleman and his descendants. In those days it afforded a good living. Over the years it got lost. Despite the revolution and other changes in the French gov't, the records of it were discovered some years ago, and the current French gov't was willing to honor the commitment. However, none of the heirs have made any claim, as it is now worth next to nothing. Inflation ueber alles! :)

OK, this unit multiplier assumption is more complicated than I thought. In OLG models, people smooth consumption over their lifetime. Therefore, in order to get a unit within-period multiplier, the lifetime multiplier applicable to the currently young has to be greater than one. If their current disposable income goes up, they will increase their consumption in the future as well as the present, so part of the multiplier effect from today's fiscal policy takes place in the future. In effect, they need to be bribed into fixing the economy by getting some extra future consumption to go along with their extra current consumption. This bribe is indeed (I think) a transfer from a future cohort. So part of the debt (the part that was a bribe rather than straightforward fiscal policy) is a burden on future generations.

I would suggest an alternative model, though, in which people live 3 periods. Young people have very little income but still want to consume. Middle aged people have a lot of income. And old people have no income. (I'm going to assume a zero interest rate.) Middle aged and old people exhibit Ricardian equivalence. Young people don't, because they're liquidity constrained. If you do a lump sum transfer from the government, young people will consume more now, but without the intent of increasing their future consumption relative to what it would have been. When they become middle aged, they will begin to exhibit Ricardian equivalence, and the spell on future generations is broken.

@Min: "If you can produce an extra 100 apples in the first period, why not later?" Because there is unemployment now (i.e., we are in a liquidity trap) but full employment later (i.e. the trap will end).

Moi: "You have created a situation in which each succeeding generation consumes a greater portion of a fixed output. Of course that will self destruct."

Adam P: "But such things do in fact happen all the time!"

Moi: "Examples, please. :)"

Adam P: "Italy, France, the UK.

"All have systems that transfer rescources from the current young to the current old and all have reached the point where the young can't/won't finance this.

Not exactly the same thing. (I did a brief web search, but did not come close to any stats that would reveal the relative proportions of consumption by generation over time.)

"Hence the decline of defined benefit pensions in the UK, the higher retirement age in France and Italy."

If anything, that makes them counterexamples. :)

In Nick's scenario the oldsters are gov't bondholders, not pensioners. They are increasingly richer and richer, yet they do not buy gov't bonds in their old age. Nor do they give any apples to their increasingly impoverished children, who are going hungry in the hopes of having too much to eat in their dotage. Parents like that are indeed burdens on their children!

It seems to me that the main difference between Krugman and Rowe is that in Rowe's world the young or middle aged buy gov't bonds, while in Krugman's world rich people buy gov't bonds. "There is a distributional issue — Bill Gates’ children may own all the debt — but that is within generations, not between generations," he says. Given Rowe's additional assumptions, but having rich people buy the bonds means that the rich consume more and more of the national output over time. (We have seen that, too!) However, since they are the bond buyers, they have no particular trouble buying gov't bonds.

Min: "It seems to me that the main difference between Krugman and Rowe is that in Rowe's world...."

Sometimes, there is indeed a difference in the underlying assumptions that generates differences in worlds/conclusions. In this case, however, there isn't. Much as I slag accounting (at times), in this case, the underlying difference really is a difference in accounting. It's a question of keeping your head straight, and making things add up, and doing the accounts for each cohort in turn.

For God knows how many decades, economists just got the accounting wrong on this whole question. It's embarrassing.

Buchanan gets the accounting right. Barro gets the accounting right too. The difference between Buchanan and Barro is a genuine difference in what they assume about people forseeing the future taxes and whether or not they make bequests. That's a real economic difference between two internally consistent worldviews.

But the old Keynesian view, which says Barro-Ricardian equivalence is wrong, *and* that there is no burden on future taxpayers, is just internally inconsistent. It doesn't make sense, accounting-wise.

Hmmm. How come the internet hasn't exploded yet? This is a BIG question: is or is not the debt a first-order burden on future generations? We ain't talking peanuts here. This is trillions. And one of us is totally wrong: either me or PK. It's not like I'm disagreeing with some no-name blogger. (OK, maybe I'm the no-name blogger, and can be ignored, sniff.) I was hoping it would explode immediately, then I could fight the good fight and then get back to grading exams.

The intuition of moving resource claims one period forward forever isn't that hard to grasp. The Old Keynesians were famously non-rigorous, but I don't think they actually ever asserted that you can reduce a debt load in the future without affecting said future generation, cet. par.

If debt that exists now exists one hundred years from now, there is no net burden on future generations for the same reason there is no net burden on the current generation – debt exists as both a liability of the government and an asset of non government (as per PK’s post). The net burden of the debt stock therefore is zero. And that holds for any addition to the debt stock, i.e. for any such flow, between now and one hundred years from now, regardless of interest rates or anything else.

If debt that exists now is paid off with taxes one hundred years from now, there is also no net burden on future generations. The government loses a liability and non government loses an asset. (The tax is the bond asset.) The net burden of the change in the debt stock therefore is zero. So the net burden associated with the flow (debt retired by taxes) is zero. And that holds for taxes required to pay off any addition to the debt stock, i.e. for any such flow, between now and one hundred years from now, regardless of interest rates or anything else.

If there is any validity to the view that there is an inherent neutrality in the idea that “we owe it to ourselves” (and there is), then there must also be validity to the view that there is an inherent neutrality in any changes in the level of what we owe to ourselves.

A tax is an asset that is passed from non-government to government. Non-government loses an asset in the same way that government loses a liability. Both the debt effect and the tax effect associated with tax retired debt are neutral. Taxes are equivalent to equity, as opposed to debt. It’s just that the government runs a negative equity capital position as a matter of course.

Ok, Professor Rowe, I don't know if this will made you feel any better, but after reading your post, I immediately ran home and (after eating dinner) wrote a post on this topic. It's part 3, because I've been writing vaguely related articles about this for about a week or so. Unfortunately, I side with Krugman, but mostly because your model relies on ever increasing welfare programs to do the heavy lifting. The same outcome could be achieved through taxation, so I think Krugman is right in that it isn't debt that burdens future generations, it's the welfare.

david: "...but I don't think they actually ever asserted that you can reduce a debt load in the future without affecting said future generation, cet. par."

Well, I think they did. I think PK just did (except for disincentive effects etc, which I ruled out by assumption).

JKH: "If debt that exists now exists one hundred years from now, there is no net burden on future generations for the same reason there is no net burden on the current generation – debt exists as both a liability of the government and an asset of non government (as per PK’s post). The net burden of the debt stock therefore is zero. And that holds for any addition to the debt stock, i.e. for any such flow, between now and one hundred years from now, regardless of interest rates or anything else."

Nick Rowe: "Sometimes, there is indeed a difference in the underlying assumptions that generates differences in worlds/conclusions. In this case, however, there isn't. Much as I slag accounting (at times), in this case, the underlying difference really is a difference in accounting. . . .

"But the old Keynesian view, which says Barro-Ricardian equivalence is wrong, *and* that there is no burden on future taxpayers, is just internally inconsistent. It doesn't make sense, accounting-wise."

Perhaps so. That is beyond my ken, since neither of you have spelled things out well enough for me to make sense of things.

However, it seems to me that you are assuming that the buyers of gov't bonds are the increasingly impoverished group. That leads to self-destruction, Mr. Phelps. ;) Krugman's remark about the children of Gates suggests to me that he is making a different assumption. I don't think that the mythical bond vigilantes are among the homeless. ;)

Maybe I am an unsophisticated rube but I don't see why this is so complicated. Once you stop thinking in grand collective aggregates it's easier to see how present debt can burden future tax payers.

To clarify the statement, it is not "we owe the debt to ourselves" it's that the American government owes it to some Americans and has given that debt to other Americans. These three groups are for the most part mutually exclusive and when the American government eventually pays the debt through taxation those that benefitted from deficit financing in the first place may not be the ones who pay it back.

When deficit financing is enjoyed by a generation who then ages out into the more lenient brackets of the progressive tax system. The younger generation does not receive the benefit but ages into the higher tax brackets as the government raises taxes to pay for the debt. What is most likely to occur is that the generation that faced low taxes had more disposable income to spend on bonds and therefore not only do they pay less taxes they receive the larger share of the bond repayment that occurs when the government repays the the debt.

Deficit financing reduces the budget constraint on the older generation and increases the budget constraint on the younger generation creating an inequality in their ability to benefit from the deficit financing and therefore the older generation is most definately placing a burden on the younger generation.

Krugman wrote:
"what we are leaving behind is promises that some of our children will pay money to other children"
Nick wrote, essentially:
"no - our children will have to pay us beucase we own the debt."

I think Krugmans point was that the level of debt today wont have an effect on the amount of resources we have in the future - and that we have the choice to distribute those resourses the way we want no matter what some paper say (otherwise i think he would see the redistribution between future children as a serious problem). Thus - whether you want to see it as an generational issus or between rich and poor the solution is pretty obvious - tax and redistribute.

I.e., it is only a burden on our children if we want it to be a burden on our children - we will have the option to choose that it will not be a burden.

Baker and Krugman explicitly refers to the time when we (the current generation) are dead.

"The reason is simple: at one point we will all be dead. That means that the ownership of our debt will be passed on to our children. If we have some huge thousand trillion dollar debt that is owed to our children, then how have we imposed a burden on them? "
http://krugman.blogs.nytimes.com/2011/12/28/debt-is-mostly-money-we-owe-to-ourselves/

Nick Rowe: "Much as I slag accounting (at times), in this case, the underlying difference {between Rowe and Krugman} really is a difference in accounting."

Really? Does Krugman make the following assumption?

"positive real interest rate and zero real growth"

Sorry for not reading carefully the first time. I got the zero real growth, but not the real interest rate. Is that not a recipe for unsustainability? Accounting has nothing to do with it, that's just crazy.

When I was 13 I ran across a problem in an old math book from the '40s or '50s: If you were to put $1 in the bank at the time of Christ earning 3% compound interest per year, how much money would you have after 2,000 years? If I have not made a mistake, my trusty calculator tells me $47 septillion. ;) Anyway, it is an astronomical number, and more money than there is on the face of the earth today. My conclusion at the time: No puedo. No bank, no gov't, could guarantee that much of an increase in purchasing power. I realized at the time that inflation could make compound interest work by reducing purchasing power. Much later I learned that economic growth could increase purchasing power in real terms. But take away inflation and economic growth and perpetual compound interest is nuts.

Cohort A lends apples to the government and receives the same apples back through a government transfer. There is no net exchange of apples within Cohort A. The government is running an apple deficit by issuing apple bonds.

Assume all people in Cohort A die simultaneously, just prior to maturity of the bonds.

Cohort B inherits the bonds.

(Any sale of bonds within Cohort A prior to this point is irrelevant. There can’t be a sale unless there is an exchange of bonds for apples, entirely within Cohort A. The apples therefore obviously must already exist for there to be a sale. So the same apples exist in the absence of the sale. The existence of those apples therefore is entirely irrelevant to the problem of analyzing government apple finance.)

The government owes apples to Cohort B at maturity of the bonds. It owes the original amount of apples borrowed plus apple interest. It refinances this apple obligation by issuing new apple bonds to cohort B. There is no net change in Cohort B’s apple position. Cohort B presents old bonds for new bonds. There is no net apple exchange required or involved, either within Cohort B or between Cohort A and Cohort B.

And so on.

Until the government pays off the apple bonds at some point, say when the bonds are held by Cohort Z, with apples.

That requires an apple tax for the outstanding amount.

Cohort Z pays the apple tax, but receives the same amount of apples back through the bond redemption. There is no net exchange of apples within Cohort Z or between Cohort (Z – 1) and Cohort Z. The government has paid off its apple debt.

None of this depends on the interest rate or anything else. It only reflects apple flows according to construction of the apple transactions.

If it’s the case that the tax and the redemption have something to do with the rate of interest and debt accumulation at the time, so be it. But such an assumption isn’t necessary. The reason could also have nothing to do with the rate of interest.

I’ll just add that if the skewed inter-generational distribution of apple consumption in your example is deemed to be a burden on Cohort C, it’s a burden that has nothing to do with government apple finance. Cohort C had the option of not selling apples for bonds prior to inheriting the bonds instead – i.e. it had the option of inheritance, which is the only other option besides buying them. C can forcibly exercise the inheritance option on B simply by not buying the bonds before inheriting them. And B can force the same on A. The result of that will be a non-skewed apple consumption distribution (allowing for interest), as per my comment above.

"Assume all people in Cohort A die simultaneously, just prior to maturity of the bonds.

Cohort B inherits the bonds."

The problem with this assumption is that you are simply assuming a cost free transfer of wealth. In reality the bond holders sell their bonds before they die (for their retirement say)and their ability to sell those bonds depends on the demand for bonds within the market. As the debt level increases there will be less and less demand for the governments debt and at some point some generation is going be stuck with the bonds and have no recourse to sell them at the price that the current generation paid previous generations for the bonds. This creates the intergenerational transfer of wealth.

Min: "However, it seems to me that you are assuming that the buyers of gov't bonds are the increasingly impoverished group."

I'm not assuming that. My point is that generation C (the grandchildren) will pay for generation A's transfer payment. Which is what PK says cannot happen.

Ian: "Maybe I am an unsophisticated rube but I don't see why this is so complicated. Once you stop thinking in grand collective aggregates it's easier to see how present debt can burden future tax payers."

Exactly. You have to disaggregate by generation/cohort.

"When deficit financing is enjoyed by a generation who then ages out into the more lenient brackets of the progressive tax system."

Or, more simply, that generation dies before the government increases taxes to pay for the deficit they created. There's no tax on the dead.

erik: "I.e., it is only a burden on our children if we want it to be a burden on our children - we will have the option to choose that it will not be a burden."

if the generation that benefitted from the deficit is already dead, it's too late to make the choice to tax them. They have consumed the deficit, and you can't get them to pay higher taxes from the grave.

wh10: if the rate of interest is *permanently less than GDP growth, then you don't need to increase future taxes. We discuss this in the comments above. That's the "No Ponzi condition". But Paul Krugman doesn't assume this, because he does talk about increased taxes.

Min: same point. Read earlier in the comments.

(On that old puzzle: if $1 in 1AD had been invested *in real capital* and reinvested etc., the rate of interest would have been lower than it actually was and the growth rate of GDP would have been higher than it actually was, so the paradox couldn't have happened. Never let mathematicians do economics!)

JKH: "Cohort B inherits the bonds."

Cohorts A and B overlap in time. A are the old guys, and B the young guys. A *sell* the bonds to B in exchange for B's apples. A eats B's apples.

JKH: "C can forcibly exercise the inheritance option on B simply by not buying the bonds before inheriting them. And B can force the same on A."

True. It would be *collectively* rational for cohort C to refuse to buy the bonds from cohort B (and for B to refuse to buy the bonds from cohort A). But it is not *individually* rational for each individual in cohort C (or B) to do this. Because if someone offers to sell me a $100 safe bond for $1 I will choose to buy it. You are assuming that the whole cohort acts together to collude as a monopsonist. The only way to get this done would be for the young people to vote in a government that defaults on the debt. In which case, whoever is holding the debt at the time of the default pays for A's transfers.

It’s still C’s choice (even considered as a collection of individuals) to buy the bonds rather than inherit them. Even if B is in a position of wanting to sell bonds for apples, nobody is forcing C to buy the bonds. C must judge the risk of taxation in light of the return available from the apple discount on the bonds it has the option of buying.

But none of that is a burden due to the nature of government finance. It’s still C’s option to hedge any tax risk in its entirety – by refusing to buy any bonds – and inheriting them instead.

Although at $ 1 on 100, (or 1 apple on 100), it’s probably not a bad bet for C to buy the bonds. And in that case, the consumption skew that is the burden is negligible.

Also, I dont think this debate is entirely about who is ripping who off. I believe what Krugman really wants to convince us of is that there is no long term cost to carrying debt in the long run.

In the household example the (responsible) household limits the amount of debt they take on because they know as soon as they stop taking on debt their wealth will be lower than it was before the debt was taken. Taking on debt to finance consumption is a net negative to the household in the long run and this is a long run that occurs well within the lifetime of the members of the household.

What Krugman wants to convince us "rubes" of is that in the case of a country there is no net negative in the long run because we are just "paying the interest to ourselves" anyway so that in the long run this cannot be a net negative on the system. Forgetting this transfer of wealth for the moment we can see that as the government goes out an looks for new demand for its debt it has to increase the interest rate that it pays to entice bond holders to get on the ponzi train.

As the interest rate increases the value of the previous bonds drop because their lower interest rates are not enough to compete with the newly minted T-bills that the government is handing out. This means that while the assets and liabilities will always equal zero in terms of T-bills they do not always equal zero in terms of dollars, ie wealth.

In the long run either the government goes bankrupt or it pays back its creditors. The interest payments go to a select few bond holders while the costs are distributed evenly among the tax payers. Now you could say that the government can increase the tax on those that recieve the extra amount but this is basically renegging on the comittment you made to pay a certain percentage when you initially issued the bond.